Contents
Preface v
1 Introductio n 1
1.1 Mar s 1
1.1.1 Motio n o f Mars 2
1.1.2 Th e
a
far out " planet s 4
1.2 Mercur y 6
1.3 Epicycle s 1
1.4 Chaoti c behavio r 13
1.4.1 Newton' s metho d 14
1.4.2 Perio d thre e an d circl e maps 19
1.4.3 Th e force d Va n de r Po l equation s 2 3
1.5 Th e ring s o f Satur n 2 6
1.5.1 Kink y behavio r 2 6
1.5.2 A model 2 7
2 Centra l configuration s 3 1
2.1 Equation s o f motion an d integral s 3 2
2.2 Centra l Configuration s 3 4
2.2.1 Wh y centra l configuration s ar e importan t 3 6
2.2.2 Valu e o f A 4 0
2.2.3 Equivalenc e classe s of configurations 4 2
2.3 A conjecture an d a velocity decompositio n 4 7
2.3.1 Viria l Theore m an d th e conjectur e 4 7
2.3.2 Th e syste m velocit y decompositio n 5 1
2.3.3 Centra l configuration s an d th e velocit y decompositio n 5 4
2.3.4 Motio n preservin g a n Eule r similarit y clas s 5 6
vn
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